A conventional sensor element for a broadband lambda probe for determining the oxygen concentration in the exhaust gas of an internal combustion engine, described in, for example, German Patent No. DE 103 05 856 A1, has a stratified structure of ceramic layers that are made up of a solid electrolyte, such as zirconium oxide (ZrO2) having proportions of silicon oxide (SiO2) and yttrium oxide (Y2O3). Between two solid electrolyte layers a gas chamber is formed, which is covered by a diffusion barrier from a gas access opening, that is inserted into the one solid electrolyte layer. A measuring electrode, or Nernst electrode, and an inner pump electrode are situated in the gas chamber. The inner pump electrode, which is situated on one solid electrolyte layer, together with an outer pump electrode that is situated on the outer side of the same solid electrolyte layer, and is exposed to the exhaust gas, forms a so-called pump cell, by which oxygen is pumped in and out of the gas chamber. The measuring electrode or Nernst electrode situated on the other solid electrolyte layer forms a measuring cell, or Nernst cell, together with a reference electrode that is exposed to a reference gas. One additional solid electrolyte layer, which is laminated together with the two other solid electrolyte layers, bears on its side lying against the one solid electrolyte layer an electrical heating element that is embedded in an insulating layer made of aluminum oxide (Al2O3) . The sensor element thus constructed is subsequently exposed to a sintering process.
In order to produce the diffusion barrier, a paste is used that is composed generally of ZrO2 having proportions of SiO2 and Y2O3, and is packed with a pore-forming material. During the sintering of the sensor element, the pore-forming material evaporates or burns, and leaves pores in the material through which the exhaust gases are able to diffuse and get into the gas chamber, during operation of the sensor element. In the process, the silicon proportion of the paste accelerates its sintering, while the yttrium proportion lowers the sintering activity. The silicon proportion in the paste is less and the yttrium proportion greater, compared to the adjoining solid electrolyte layers. Because of the sintering activity in the paste that is diminished thereby, a size reduction or a closing of the pores, left behind by the pore-forming material after it is burned out, is damped. During the sintering of the sensor element, the greater silicon proportion of the solid electrolyte layer also influences the sintering activity in the paste of the diffusion barrier. In the border areas of the diffusion barrier that adjoin the solid electrolyte layers, there will be greater sintering, in this context, than in the middle areas, which will result in smaller pores in the border area. Whereas in thick diffusion barriers the percentage proportion of more greatly sintered border areas is low at the entire diffusion barrier, the more greatly sintered border areas, in the case of thin diffusion barriers, have a nonnegligible effect on the static pressure dependence of the diffusion barrier, because the smaller pores, whose diameter is smaller than the free path of the gas molecules, increase the proportion of Knudsen diffusion, and thus the proportion of the static pressure dependence of the oxygen transport by the solid electrolyte. This leads to an uncontrolled variation in the useful signal of the sensor element.